To estimate proportions in the domains, one can consider explicit linking models based on auxiliary data aggregated to the domain level. A popular model is the Fay–Herriot (FH) model, which is a separate case of linear mixed models, and the empirical best linear unbiased predictors (EBLUPs) of the domain means or proportions are derived from it [1]}. That small area predictor is expressed as the linear combination of a regression-synthetic estimator and the direct estimator. While the former part accounts for a variation reflected in the auxiliary data, the direct component exploits the unbiasedness property. Compositions of the synthetic and the direct estimators constitute an important class of indirect estimators. Before the mixed models, traditional design-based composite estimators were often used [2]}. However, now it is accepted that the models including random area-specific effects are more useful. For example, they are more convenient to handle complex data structures than the traditional estimators with only randomness induced by the sampling design. Another notable drawback of the latter estimators is the difficulty in estimating their precision. The problem is with bias estimation, while it is well elaborated for the estimators like EBLUP.
